시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
7 초 128 MB 4287 66 43 9.267%

문제

Brainf**k 프로그램이 주어졌을 때, 이 프로그램이 끝나는지, 무한 루프에 빠지는지 알아내는 프로그램을 작성하시오.

무한 루프란, 특정 시점부터 탈출하지 않고 무한히 반복 실행되는 루프를 말한다.

Brainf**k 인터프리터는 정수를 담는 하나의 배열(unsigned 8-bit 정수)과, 그 배열의 칸 하나를 가리키는 포인터로 이루어져 있다. Brainf**k 프로그램은 다음과 같이 8개의 명령어로 이루어져 있다.

- 포인터가 가리키는 수를 1 감소시킨다. (modulo 28)
+ 포인터가 가리키는 수를 1 증가시킨다. (modulo 28)
< 포인터를 왼쪽으로 한 칸 움직인다.
> 포인터를 오른쪽으로 한 칸 움직인다.
[ 만약 포인터가 가리키는 수가 0이라면, [ 와 짝을 이루는 ] 의 다음 명령으로 점프한다.
] 만약 포인터가 가리키는 수가 0이 아니라면, ] 와 짝을 이루는 [ 의 다음 명령으로 점프한다.
. 포인터가 가리키는 수를 출력한다.
, 문자 하나를 읽고 포인터가 가리키는 곳에 저장한다. 입력의 마지막(EOF)인 경우에는 255를 저장한다.

인터프리터는 Brainf**k 프로그램의 첫 번째 명령부터 수행하고, 더이상 수행할 명령이 없다면, 프로그램을 종료한다. 각 명령을 수행하고 나면, 다음 명령을 수행한다. 물론 [이나 ]인 경우에는 다음 명령으로 이동하는 것이 아니라 점프를 한다.

데이터 배열의 크기는 문제에서 주어지는 값을 사용해야 한다. 또, 데이터 배열의 값이 underflow나 overflow를 일으켰을 때는 일반적인 방법을 따르면 된다. 프로그램을 수행하기 전에, 데이터 배열의 값은 0으로 초기화되어 있고, 포인터가 가리키는 칸은 0번 칸이다.

포인터를 왼쪽이나 오른쪽으로 움직일 때, 데이터 배열의 범위를 넘어간다면, 반대쪽으로 넘어가게 된다. 즉, 포인터가 0을 가리킬 때, 1을 감소시킨다면, 배열의 크기 - 1번째를 가리키게 된다.

[]는 루프를 의미하며, 중첩될 수 있다. 입력으로 주어진 프로그램은 잘 짜여 있음이 보장된다. 즉 프로그램을 왼쪽에서 오른쪽으로 훑으면서 [의 개수에서 ]의 개수를 빼면 항상 0보다 크거나 같고, 맨 끝까지 훑으면 그 값은 0이 된다.

이 문제는 Brainf**k 프로그램이 무한 루프에 빠지는지 안 빠지는지를 검사하기만 하면 된다. 따라서, 출력은 무시한다.

입력

첫째 줄에 테스트 케이스의 개수 t (0 < t ≤ 20)가 주어진다. 각 테스트 케이스는 세 줄로 이루어져 있다. 첫째 줄에는 sm, sc, si가 주어진다. sm은 메모리(배열)의 크기이고, sc는 프로그램 코드의 크기, si는 입력의 크기이다. (0 < sm ≤ 100,000, 0 < sc, si < 4096)

둘째 줄에는 Brainf**k 프로그램이 주어진다. 프로그램은 sc개의 문자로 이루어져 있다.

셋째 줄에는 프로그램의 입력이 주어진다. (공백이 아니면서 출력할 수 있는 문자만 주어진다)

출력

각 테스트 케이스에 대해서, 프로그램이 종료된다면 "Terminates"를, 무한 루프에 빠지게 된다면 "Loops"를 출력한다. 무한 루프에 빠졌을 때는, 프로그램의 어느 부분이 무한 루프인지를 출력한다. ([]의 위치) 프로그램이 명령어를 50,000,000번 이상 수행한 경우, 프로그램은 항상 종료되었거나 무한 루프에 빠져있다. 무한 루프일 경우, 해당 루프는 적어도 한 번 실행이 완료된 상태이며, 한 번의 무한 루프에서 실행되는 명령어의 개수는 50,000,000개 이하이다.

예제 입력 1

4
10 4 3
+-.,
qwe
1000 5 1
+[+-]
a
100 74 4
+++++[->++<]>[-<+++++++>]<[->+>+>+>+<<<<]>+++>--->++++++++++>---<<<.>.>.>.
xxyz
9999 52 14
+++++[>+++++++++<-],+[-[>--.++>+<<-]>+.->[<.>-]<<,+]
this_is_a_test

예제 출력 1

Terminates
Loops 1 4
Terminates
Terminates
[{"problem_id":"3954","problem_lang":"0","title":"Brainf**k \uc778\ud130\ud504\ub9ac\ud130","description":"<p>Brainf**k \ud504\ub85c\uadf8\ub7a8\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc774 \ud504\ub85c\uadf8\ub7a8\uc774 \ub05d\ub098\ub294\uc9c0, \ubb34\ud55c \ub8e8\ud504\uc5d0 \ube60\uc9c0\ub294\uc9c0 \uc54c\uc544\ub0b4\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\ubb34\ud55c \ub8e8\ud504\ub780, \ud2b9\uc815 \uc2dc\uc810\ubd80\ud130 \ud0c8\ucd9c\ud558\uc9c0 \uc54a\uace0 \ubb34\ud55c\ud788 \ubc18\ubcf5 \uc2e4\ud589\ub418\ub294 \ub8e8\ud504\ub97c \ub9d0\ud55c\ub2e4.<\/p>\r\n\r\n<p>Brainf**k \uc778\ud130\ud504\ub9ac\ud130\ub294 \uc815\uc218\ub97c \ub2f4\ub294 \ud558\ub098\uc758 \ubc30\uc5f4(unsigned 8-bit \uc815\uc218)\uacfc, \uadf8 \ubc30\uc5f4\uc758 \uce78 \ud558\ub098\ub97c \uac00\ub9ac\ud0a4\ub294 \ud3ec\uc778\ud130\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. Brainf**k \ud504\ub85c\uadf8\ub7a8\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 8\uac1c\uc758 \uba85\ub839\uc5b4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:100%\">\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<th style=\"width:20%\"><code>-<\/code><\/th>\r\n\t\t\t<td style=\"width:80%\">\ud3ec\uc778\ud130\uac00 \uac00\ub9ac\ud0a4\ub294 \uc218\ub97c 1 \uac10\uc18c\uc2dc\ud0a8\ub2e4. (modulo 2<sup>8<\/sup>)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th><code>+<\/code><\/th>\r\n\t\t\t<td>\ud3ec\uc778\ud130\uac00 \uac00\ub9ac\ud0a4\ub294 \uc218\ub97c 1 \uc99d\uac00\uc2dc\ud0a8\ub2e4. (modulo 2<sup>8<\/sup>)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th><code>&lt;<\/code><\/th>\r\n\t\t\t<td>\ud3ec\uc778\ud130\ub97c \uc67c\ucabd\uc73c\ub85c \ud55c \uce78 \uc6c0\uc9c1\uc778\ub2e4.<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th><code>&gt;<\/code><\/th>\r\n\t\t\t<td>\ud3ec\uc778\ud130\ub97c \uc624\ub978\ucabd\uc73c\ub85c \ud55c \uce78 \uc6c0\uc9c1\uc778\ub2e4.<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th><code>[<\/code><\/th>\r\n\t\t\t<td>\ub9cc\uc57d \ud3ec\uc778\ud130\uac00 \uac00\ub9ac\ud0a4\ub294 \uc218\uac00 0\uc774\ub77c\uba74,&nbsp;<code data-stringify-type=\"code\">[<\/code>&nbsp;\uc640 \uc9dd\uc744 \uc774\ub8e8\ub294&nbsp;<code data-stringify-type=\"code\">]<\/code>&nbsp;\uc758 \ub2e4\uc74c \uba85\ub839\uc73c\ub85c \uc810\ud504\ud55c\ub2e4.<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th><code>]<\/code><\/th>\r\n\t\t\t<td>\ub9cc\uc57d \ud3ec\uc778\ud130\uac00 \uac00\ub9ac\ud0a4\ub294 \uc218\uac00 0\uc774 \uc544\ub2c8\ub77c\uba74,&nbsp;<code data-stringify-type=\"code\">]<\/code>&nbsp;\uc640 \uc9dd\uc744 \uc774\ub8e8\ub294&nbsp;<code data-stringify-type=\"code\">[<\/code>&nbsp;\uc758 \ub2e4\uc74c \uba85\ub839\uc73c\ub85c \uc810\ud504\ud55c\ub2e4.<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>.<\/th>\r\n\t\t\t<td>\ud3ec\uc778\ud130\uac00 \uac00\ub9ac\ud0a4\ub294 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>,<\/th>\r\n\t\t\t<td>\ubb38\uc790 \ud558\ub098\ub97c \uc77d\uace0 \ud3ec\uc778\ud130\uac00 \uac00\ub9ac\ud0a4\ub294 \uacf3\uc5d0 \uc800\uc7a5\ud55c\ub2e4. \uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9(EOF)\uc778 \uacbd\uc6b0\uc5d0\ub294 255\ub97c \uc800\uc7a5\ud55c\ub2e4.<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>\uc778\ud130\ud504\ub9ac\ud130\ub294 Brainf**k \ud504\ub85c\uadf8\ub7a8\uc758 \uccab \ubc88\uc9f8 \uba85\ub839\ubd80\ud130 \uc218\ud589\ud558\uace0, \ub354\uc774\uc0c1 \uc218\ud589\ud560 \uba85\ub839\uc774 \uc5c6\ub2e4\uba74, \ud504\ub85c\uadf8\ub7a8\uc744 \uc885\ub8cc\ud55c\ub2e4. \uac01 \uba85\ub839\uc744 \uc218\ud589\ud558\uace0 \ub098\uba74, \ub2e4\uc74c \uba85\ub839\uc744 \uc218\ud589\ud55c\ub2e4.&nbsp;\ubb3c\ub860 <code>[<\/code>\uc774\ub098 <code>]<\/code>\uc778 \uacbd\uc6b0\uc5d0\ub294 \ub2e4\uc74c \uba85\ub839\uc73c\ub85c \uc774\ub3d9\ud558\ub294 \uac83\uc774 \uc544\ub2c8\ub77c \uc810\ud504\ub97c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub370\uc774\ud130 \ubc30\uc5f4\uc758 \ud06c\uae30\ub294 \ubb38\uc81c\uc5d0\uc11c \uc8fc\uc5b4\uc9c0\ub294 \uac12\uc744 \uc0ac\uc6a9\ud574\uc57c \ud55c\ub2e4. \ub610, \ub370\uc774\ud130 \ubc30\uc5f4\uc758 \uac12\uc774 underflow\ub098 overflow\ub97c \uc77c\uc73c\ucf30\uc744 \ub54c\ub294 \uc77c\ubc18\uc801\uc778 \ubc29\ubc95\uc744 \ub530\ub974\uba74 \ub41c\ub2e4. \ud504\ub85c\uadf8\ub7a8\uc744 \uc218\ud589\ud558\uae30 \uc804\uc5d0, \ub370\uc774\ud130 \ubc30\uc5f4\uc758 \uac12\uc740 0\uc73c\ub85c \ucd08\uae30\ud654\ub418\uc5b4 \uc788\uace0, \ud3ec\uc778\ud130\uac00 \uac00\ub9ac\ud0a4\ub294 \uce78\uc740 0\ubc88 \uce78\uc774\ub2e4.<\/p>\r\n\r\n<p>\ud3ec\uc778\ud130\ub97c \uc67c\ucabd\uc774\ub098 \uc624\ub978\ucabd\uc73c\ub85c \uc6c0\uc9c1\uc77c \ub54c, \ub370\uc774\ud130 \ubc30\uc5f4\uc758 \ubc94\uc704\ub97c \ub118\uc5b4\uac04\ub2e4\uba74, \ubc18\ub300\ucabd\uc73c\ub85c \ub118\uc5b4\uac00\uac8c \ub41c\ub2e4. \uc989, \ud3ec\uc778\ud130\uac00 0\uc744 \uac00\ub9ac\ud0ac \ub54c, 1\uc744 \uac10\uc18c\uc2dc\ud0a8\ub2e4\uba74, \ubc30\uc5f4\uc758 \ud06c\uae30 - 1\ubc88\uc9f8\ub97c \uac00\ub9ac\ud0a4\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p><code>[<\/code>\uc640 <code>]<\/code>\ub294 \ub8e8\ud504\ub97c \uc758\ubbf8\ud558\uba70, \uc911\ucca9\ub420 \uc218 \uc788\ub2e4. \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \ud504\ub85c\uadf8\ub7a8\uc740 \uc798 \uc9dc\uc5ec \uc788\uc74c\uc774 \ubcf4\uc7a5\ub41c\ub2e4. \uc989 \ud504\ub85c\uadf8\ub7a8\uc744 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \ud6d1\uc73c\uba74\uc11c <code>[<\/code>\uc758 \uac1c\uc218\uc5d0\uc11c <code>]<\/code>\uc758 \uac1c\uc218\ub97c \ube7c\uba74 \ud56d\uc0c1 0\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, \ub9e8 \ub05d\uae4c\uc9c0 \ud6d1\uc73c\uba74 \uadf8 \uac12\uc740 0\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc774 \ubb38\uc81c\ub294 Brainf**k \ud504\ub85c\uadf8\ub7a8\uc774 \ubb34\ud55c \ub8e8\ud504\uc5d0 \ube60\uc9c0\ub294\uc9c0 \uc548 \ube60\uc9c0\ub294\uc9c0\ub97c \uac80\uc0ac\ud558\uae30\ub9cc \ud558\uba74 \ub41c\ub2e4. \ub530\ub77c\uc11c, \ucd9c\ub825\uc740 \ubb34\uc2dc\ud55c\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 t (0 &lt; t &le; 20)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \uc138 \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uccab\uc9f8 \uc904\uc5d0\ub294 s<sub>m<\/sub>, s<sub>c<\/sub>, s<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. s<sub>m<\/sub>\uc740 \uba54\ubaa8\ub9ac(\ubc30\uc5f4)\uc758 \ud06c\uae30\uc774\uace0, s<sub>c<\/sub>\ub294 \ud504\ub85c\uadf8\ub7a8 \ucf54\ub4dc\uc758 \ud06c\uae30, s<sub>i<\/sub>\ub294 \uc785\ub825\uc758 \ud06c\uae30\uc774\ub2e4. (0 &lt; s<sub>m<\/sub> &le; 100,000, 0 &lt; s<sub>c<\/sub>, s<sub>i<\/sub> &lt; 4096)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 Brainf**k \ud504\ub85c\uadf8\ub7a8\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ud504\ub85c\uadf8\ub7a8\uc740 s<sub>c<\/sub>\uac1c\uc758 \ubb38\uc790\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc14b\uc9f8 \uc904\uc5d0\ub294 \ud504\ub85c\uadf8\ub7a8\uc758 \uc785\ub825\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (\uacf5\ubc31\uc774 \uc544\ub2c8\uba74\uc11c \ucd9c\ub825\ud560 \uc218 \uc788\ub294 \ubb38\uc790\ub9cc \uc8fc\uc5b4\uc9c4\ub2e4)<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \ud504\ub85c\uadf8\ub7a8\uc774 \uc885\ub8cc\ub41c\ub2e4\uba74 &quot;Terminates&quot;\ub97c, \ubb34\ud55c \ub8e8\ud504\uc5d0 \ube60\uc9c0\uac8c \ub41c\ub2e4\uba74 &quot;Loops&quot;\ub97c \ucd9c\ub825\ud55c\ub2e4. \ubb34\ud55c \ub8e8\ud504\uc5d0 \ube60\uc84c\uc744 \ub54c\ub294, \ud504\ub85c\uadf8\ub7a8\uc758 \uc5b4\ub290 \ubd80\ubd84\uc774 \ubb34\ud55c \ub8e8\ud504\uc778\uc9c0\ub97c \ucd9c\ub825\ud55c\ub2e4. (<code>[<\/code>\uc640 <code>]<\/code>\uc758 \uc704\uce58) \ud504\ub85c\uadf8\ub7a8\uc774 \uba85\ub839\uc5b4\ub97c 50,000,000\ubc88 \uc774\uc0c1 \uc218\ud589\ud55c \uacbd\uc6b0, \ud504\ub85c\uadf8\ub7a8\uc740 \ud56d\uc0c1 \uc885\ub8cc\ub418\uc5c8\uac70\ub098 \ubb34\ud55c \ub8e8\ud504\uc5d0 \ube60\uc838\uc788\ub2e4. \ubb34\ud55c \ub8e8\ud504\uc77c \uacbd\uc6b0, \ud574\ub2f9 \ub8e8\ud504\ub294 \uc801\uc5b4\ub3c4 \ud55c \ubc88 \uc2e4\ud589\uc774 \uc644\ub8cc\ub41c \uc0c1\ud0dc\uc774\uba70, \ud55c \ubc88\uc758 \ubb34\ud55c \ub8e8\ud504\uc5d0\uc11c \uc2e4\ud589\ub418\ub294 \uba85\ub839\uc5b4\uc758 \uac1c\uc218\ub294 50,000,000\uac1c \uc774\ud558\uc774\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"3954","problem_lang":"1","title":"BrainF**kVM","description":"<p>Given a brainf**k program, determine whether it terminates or enters an endless loop.<\/p>\r\n\r\n<p>A brainf**k interpreter has a data array (consisting of unsigned 8-bit integers) with an index, the so called &quot;data index&quot;; the entry of the array pointed to by the data index is the so called &quot;current entry&quot;. A brainf**k program consists of a sequence of the following eight instructions:<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:100%\">\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<th style=\"width:20%\">-<\/th>\r\n\t\t\t<td style=\"width:80%\">decrease current entry by 1 (modulo 2<sup>8<\/sup>)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>+<\/th>\r\n\t\t\t<td>increase current entry by 1 (modulo 2<sup>8<\/sup>)<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>&lt;<\/th>\r\n\t\t\t<td>decrease data index by 1<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>&gt;<\/th>\r\n\t\t\t<td>increase data index by 1<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>[<\/th>\r\n\t\t\t<td>jump behind the matching ], if the current entry is equal to 0<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>]<\/th>\r\n\t\t\t<td>jump behind the matching [ if the current entry is not equal to 0<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>.<\/th>\r\n\t\t\t<td>print the current entry as character<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>,<\/th>\r\n\t\t\t<td>read a character and save it into the current entry. On end of input save 255.<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>Interpretation of a brainf**k program starts at the first instruction, and terminates if the instruction pointer leaves the end of the program. After an instruction is executed, the instruction pointer advances to the instruction to the right (except, of course, if the loop instructions [ or ] cause a jump).<\/p>\r\n\r\n<p>In addition to the program, you will be given the size of the data array. The entries of the data array shall be unsigned 8-bit integers, with usual over- or underflow behaviour. At the start of the<\/p>\r\n\r\n<p>program, the data array entries and the data index shall be initialized to zero. Incrementing or decrementing the data index beyond the boundaries of the data array shall make it re-enter the data array at the other boundary; e.g. decrementing the data index when it is zero shall set it to the size of the data array minus one.<\/p>\r\n\r\n<p>The [ and ] instructions define loops and are allowed to nest. Every given program will be wellformed, i.e. when traversing the program from left to right, the number of [ instructions minus the number of ] instructions will always be greater or equal zero, and at the end of the program it will be equal to zero.<\/p>\r\n\r\n<p>For the purposes of the problem, discard the output of the interpreted program.&nbsp;<\/p>\r\n","input":"<p>The input starts with a line containing the number of test cases t (0 &lt; t &le; 20). Each test case consists of three lines. The first line contains three integers s<sub>m<\/sub>, s<sub>c<\/sub>, s<sub>i<\/sub>, describing the size of the memory, the size of the program code and the size of the input (0 &lt; s<sub>m<\/sub> &le; 100 000; 0 &lt; s<sub>c<\/sub>, s<sub>i<\/sub> &lt; 4 096). The second line contains the brainf**k program code to be executed; it consists of s<sub>c<\/sub> characters. The third line contains the input of the program, as text (only printable, non-whitespace characters).<\/p>\r\n\r\n<p>Once the program has consumed all available input, the input instruction shall set the current cell to 255.<\/p>\r\n","output":"<p>For each test case, print one line, containing either &quot;Terminates&quot; or &quot;Loops&quot;, depending on whether the program either terminates after a finite number of steps, or enters an endless loop. If the program loops, also print the indices (0-based) of the two [ and the ] symbols in the code array that correspond to the endless loop. You may safely assume that after 50 000 000 instructions, a program either terminated or hangs in an endless loop, which then was executed at least once. During each iteration of the endless loop at most 50 000 000 instructions are executed.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Europe > Northwestern European Regional Contest > German Collegiate Programming Contest > GCPC 2012 B번

  • 문제를 번역한 사람: baekjoon
  • 데이터를 추가한 사람: dojujh05013
  • 빠진 조건을 찾은 사람: jh05013
  • 문제를 다시 작성한 사람: jh05013